Question

Consider the following scenario analysis:
				Rate of Return
Scenario	Probability			Stocks	Bonds
Recession	0.2			-6%	17%
Normal Economy	0.6			19%	9%
Boom	0.2			30%	5%
1) Is it reasonable to assume that Treasury bonds will provide higher returns in recessions that in booms? Yes or No
2) Calculate the expected rate of return and standard deviation for each investment
	Expected Rate of Return			Standard Deviation
Stocks			%		%
Bonds			%		%
3) Which investment would you prefer? And how would you classify each?
Stocks	Bonds
More risk-averse	More risk-averse
Less risk averse	Less risk averse
risk- neutral	risk- neutral

Answer 1

1) Yes during recession returns go up. This is because in recession demand for treasury bond increases and prices go up. This leads to gain due to capital appreciation of bonds.

2) Expected Return of Stock =0.2*-6%+0.6*19%+0.2*30% =16.2%
Standard Deviation of Stock =(0.2*(-6%-16.2%)^2+0.6*(19%-16.2%)^2+0.2*(30%-16.2%)^2)^0.5 =11.89%
Expected Return of Bond=0.2*17%+0.6*9%+0.2*5% =9.80%
Standard Deviation of Bond =(0.2*(17%-9.80%)^2+0.6*(9%-9.80%)^2+0.2*(5%-9.80%)^2)^0.5 =3.92%

3) Coefficient of Variation of Stock =Standard Deviation of Stock/Expected Return of Stock =11.89%/16.20% =0.73
Coefficient of Variation of Bond=Standard Deviation of Stock/Expected Return of Stock =3.92%/9.80% =0.40
Bonds should be preferred.

Stock are less risk averse.
Bond are more risk averse.